Problem: Simplify the following expression: $\dfrac{44k^5}{22k^2}$ You can assume $k \neq 0$.
Answer: $ \dfrac{44k^5}{22k^2} = \dfrac{44}{22} \cdot \dfrac{k^5}{k^2} $ To simplify $\frac{44}{22}$ , find the greatest common factor (GCD) of $44$ and $22$ $44 = 2 \cdot 2 \cdot 11$ $22 = 2 \cdot 11$ $ \mbox{GCD}(44, 22) = 2 \cdot 11 = 22 $ $ \dfrac{44}{22} \cdot \dfrac{k^5}{k^2} = \dfrac{22 \cdot 2}{22 \cdot 1} \cdot \dfrac{k^5}{k^2} $ $\phantom{ \dfrac{44}{22} \cdot \dfrac{5}{2}} = 2 \cdot \dfrac{k^5}{k^2} $ $ \dfrac{k^5}{k^2} = \dfrac{k \cdot k \cdot k \cdot k \cdot k}{k \cdot k} = k^3 $ $ 2 \cdot k^3 = 2k^3 $